Question

Rationalize the denominator and simplify: sqrtb/sqrtb-3

Answer 1

To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator.

sqrt(b) / sqrt(b - 3)

= sqrt(b) / sqrt(b - 3) * (sqrt(b) + sqrt(b - 3)) / (sqrt(b) + sqrt(b - 3))

= (sqrt(b) * sqrt(b) + sqrt(b) * sqrt(b - 3)) / (sqrt(b) * sqrt(b) + sqrt(b) * sqrt(b - 3) - sqrt(b - 3) * sqrt(b) - sqrt(b - 3) * sqrt(b - 3))

= (b + sqrt(b^2 - 3b)) / (b + b - 3)

= (b + sqrt(b^2 - 3b)) / (2b - 3)

So, the simplified expression is (b + sqrt(b^2 - 3b)) / (2b - 3).